A maker of a certain brand of low fat cereal bars claims that the average saturated fat content is 0.5 grams. To check the claim, a random sample of 9 cereal bars of this brand were drawn, and the sample mean and sample standard deviation was found to be 0.52 and 0.2, respectively. If the computed t-value falls between -talpha/2 and talpha/2, the maker is satisfied with the claim. (t0.05=1.860 for df=8).
a) What is the sampling distribution of the sample mean Xbar?
b) Use the sampling distribution to find P(Xbar> 0.52).